A method for utilizing surface photo voltage (hereinafter, referred to as SPV) is proposed as a method for measuring resistivity of a semiconductor wafer in a noncontact manner by Emil Kamieniecki et al, for example, in J. Appl. Phys. Vol. 54 (11), November 1983, p. 6481. The SPV means a change in surface potential produced when a semiconductor is irradiated with light. The SPV excited by the use of a photon beam intermittently chopped at an appropriate frequency as incident light is called alternating current SPV (AC-SPV). In the present specification, the SPV means the AC-SPV, unless otherwise specified.
First, one example of a device for measuring the SPV will be described with reference to FIG. 4. In FIG. 4, reference numeral 10 denotes a device for measuring the SPV. A light emitting diode 12 (hereinafter, referred to as an LED) is usually used as its light source because it is intermittently chopped with ease. Light 12a of the LED 12 chopped at an appropriate frequency is converged through an aperture 14 and a lens 16 and applied to the surface of an Si wafer W. Reference numeral 18 denotes an LED driver that drives the LED 12 and is connected to a lock-in amplifier 20. The AC-SPV is measured by the lock-in amplifier 20 synchronized with a driving frequency of the LED connected to a transparent electrode 24 placed on the Si wafer W with a Mylar film 22 interposed between them. The Mylar film 22 is not necessarily provided but the AC-SPV can be also measured by the transparent electrode 24 placed on the surface of the Si wafer W via an air gap of about from several tens μm to 200 μm. The transparent electrode 24 can be formed, for example, by evaporating indium oxide on a glass substrate. Here, reference numeral 26 denotes a glass plate placed on the upper surface of the transparent electrode 24 and reference numeral 28 denotes a metal electrode, respectively.
Taking a p-type Si wafer as an example, the principle of measuring resistivity of the wafer is shown in FIG. 5. In the case where the positive charge Qs (Qs>0) is present on the surface of the Si wafer W, free holes near the surface of a bulk are electrostatically repulsed by the positive charge thereby to be pressed into the bulk. As a result, only acceptor atoms negatively ionized appear near the surface and hence the negative charge Qsc (Qsc<0) is formed. A region where the free holes are not present, that is, a depletion layer region 36 is formed near the surface of the bulk. An inner electric field is formed in this depletion layer region 36 by the positive charge Qs on the surface and the negative charge Qsc in the Si bulk. A transparent electrode 30 for measuring the AC-SPV is placed on the Si wafer W via an air gap 32 of 100 μm in thickness. This construction enables advantageously to measure the AC-SPV in a manner of noncontact with the surface of the Si wafer. Light having a wavelength shorter than a wavelength corresponding to an energy gap of Si is used as incident light 34a [chopped intermittent light of 40 KHz to 50 KHz] from a light source 34. The reason why light having such a short wavelength is used is given as follows.
For example, in the case of light having a wavelength of 450 nm, it has a large absorption coefficient in Si and hence it enters the Si wafer to a depth of about 0.5 μm. If the width of the depletion layer 36 formed near the surface of the Si wafer W is 1 μm, all of the incident light is absorbed in the depletion layer 36. As a result, excessive carriers excited in the Si wafer by the incident light are generated only in the depletion layer 36.
The excessive carriers [electron (e), hole (h)] excited in the depletion layer 36 are separated in terms of their electric charge only by the inner electric field. Thus, the obtained SPV is not affected by the substrate characteristics such as the carrier diffusion length L and the surface recombination rate on a back surface of the Si wafer and hence a photoelectric current Jph is expressed by the following equation.Jph=qΦ(1−R)  (1)
where q is the elementary quantity of the electric charge, Φ is the incident photon density, and R is the optical reflection factor.
When the surface of a specimen is uniformly irradiated with the light in this state, the AC-SPV can be expressed by the following equation (for example, Emil Kamieniecki et al, J. Appl. Phys. Vol. 54 (11), November 1983, p. 6481).δVs=−jδφω−1(1−R)q Cdp−1  (2)
where Vs is the electric potential barrier height of the surface, ω is the angular frequency of the incident light (ω=2πf, where f is the modulation frequency), q is the elementary quantity of the electric charge, Cdp is the capacitance of the depletion layer formed on the surface of the specimen, R is the optical reflection factor, and φ is the incident photon flux. δVs is a change in Vs that is observed as AC-SPV in the transparent electrode 30 placed on the specimen in FIG. 5 via the air gap 32 of about 100 μm in thickness. Note that, in FIG. 5, reference numeral 38 denotes a ground electrode.
The general dependence of the AC-SPV on a modulation frequency measured under conditions in which excessive carriers are generated only in the depletion layer 36 in this manner is shown in FIG. 6. In order to describe the AC-SPV, some people try to use an equivalent circuit. For example, R. S. Nakhmason, et al., Solid-St. Electron, 18 (1975), pp. 627-634, and C. Munakata et al., Jpn. J. A. P. 23, (1984), pp. 1451-1460 are mentioned. An equivalent circuit in the case where a strong inversion layer is formed on the surface of the semiconductor, which is proposed by C. Munakata et al., is shown as one example in FIG. 7. It is generally known that the respective states of a neutral state, a depletion state, a weak inversion state, and a strong inversion state can be produced on the surface of the semiconductor by the use of surface treatment.
Here, the AC-SPV signal shown in FIG. 6 will be described only for the strong inversion state by the use of the equivalent circuit. This is because a conventional technique for measuring resistivity by the use of the AC-SPV is constructed based on a theory premised on the strong inversion state. The detailed description of the equivalent circuit will not be made here because the above papers describe the equivalent circuit. In FIG. 7, Cin is the inversion layer capacitance, gin is the inversion layer conductance, Cdp is the depletion layer capacitance, and gdp is the depletion layer capacitance. The AC-SPV is expressed in the following equations by the use of the equivalent circuit.δVs=δJph|Z|  (3)Z=1/(gin+gdp+jω(Cin+Cdp))  (4)
where Vs is the electric potential barrier height, Jph is the photoelectric current, and Z is the impedance.
As is evident from the equivalent circuit, the equivalent circuit is a parallel circuit of the capacitance and the resistance. Therefore, the SPV limited by the conductance gin and gdp appears in a region where the modulation frequency of the incident light is low. It is understood that the SPV takes a constant value, irrespective of the modulation frequency, in this region (a region “A” in FIG. 6, which is hereinafter referred to as a low frequency region).
Conversely, in a region where the modulation frequency is high (a region “B” in FIG. 6, which is hereinafter referred to as a high frequency region), it is understood that the observed SPV signal is inversely proportional to the modulation frequency f because the AC-SPV is limited by the capacitance Cin and Cdp. An intermediate region of the modulation frequency between both of the regions (a region “C” in FIG. 6, which is hereinafter referred to as a transition frequency region) is a transition region from the region limited by the conductance to the region limited by the capacitance.
As is clear from the above description, if there is measured the AC-SPV signal in the region of the high modulation frequency in which the AC-SPV signal is proportional to the reciprocal of the modulation frequency f, the combined capacitance of Cin and Cdp, which is a capacitance component formed on the surface of the specimen, can be measured from the observed AC-SPV signal. Because of Cin<<Cdp in the strong inversion state, the observed AC-SPV signal depends only on Cdp. As a result, the depletion layer capacitance can be calculated. In general, the following equation is established between the depletion layer capacitance Cdp and the depletion layer width Wd.Cdp=∈s/Wd  (5)
where ∈s is the relative dielectric constant of Si.
Therefore, if there is measured the AC-SPV signal in the region of the high modulation frequency in which the AC-SPV signal is proportional to the reciprocal of the modulation frequency f, the depletion layer capacitance Cdp of the object to be measured (Si) can be calculated from the equation (2). Further, from the equation (5), the depletion layer width Wd can be calculated. If the surface of the object to be measured is in the strong inversion state, the depletion layer width Wd becomes a maximum value Wmax and can be expressed by the following equation.Wmax=√{square root over (4∈skT ln(Nsc/ni)/(q2Nsc))}{square root over (4∈skT ln(Nsc/ni)/(q2Nsc))}  (6)
where Wmax is the maximum depletion layer width in the strong inversion state, ∈s is the relative dielectric constant of Si, k is the Boltzmann constant, Nsc is the dopant concentration, ni is the intrinsic carrier density of Si, and q is the elementary quantity of the electric charge, respectively.
The dopant concentration of the object to be measured can be calculated by the use of this equation. A commercially available device for measuring resistivity of an Si wafer by the use of the AC-SPV, for example, a resistivity measuring device commercially sold by QC Solutions, Inc. (under a trade name of “SCP”) uses light with a wavelength of 450 nm that is chopped (at a chopping frequency of 40 kHz) as incident light. In this device, excessive carriers generated by irradiating light can be generated only in the depletion layer and the chopping frequency of 40 kHz is in the region where the AC-SPV signal is inversely proportional to the chopping frequency f. Thus, as described above, the device can measure the depletion layer capacitance.
In this device, in the case of measuring a p-type Si wafer, the Si wafer is subjected to treatment called ROST (Rapid Optical Surface Treatment) as pretreatment before measurement. In this ROST, the Si wafer is rapidly heated at a temperature of about 300° C. for about 30 seconds by a halogen lamp. It is assumed that the positive charge is generated on the surface of the specimen by this pretreatment to bring the surface into the strong inversion state. In the case where the surface of the specimen is in the strong inversion state, as described above, the dopant concentration of the object to be measured can be calculated from Cdp. The dopant concentration can be converted to resistivity according to ASTM (F723-81). As a result, resistivity can be calculated in principle.
However, according to the result obtained when the present inventor measured the surface state of the wafer subjected to the ROST, it was found that since the surface was not in the strong inversion state but in the depletion state or in the weak inversion state, the correct measurement result was not always obtained.
In order to solve this problem, a method for bringing the surface of the specimen into the strong inversion state can be considered. For example, in the case of the p-type Si wafer, it is enough that a considerable amount of the positive charge is generated on the surface of the Si wafer. Specific methods for generating the positive charge on the surface of the Si wafer include not only the above-mentioned ROST but also (1) dipping of the wafer in an HF water solution (C. Munakata, Semicond. Sci. Technol., 5 (1990), pp. 842-846, and (2) thermally oxidizing of the wafer (B. E. Deal, IEEE Trans. Electron Device, ED-27, (1980), pp. 606-608 and others).
However, according to the method (1), the positive charge is generated but the surface of the wafer is not brought into the strong inversion state either. Moreover, according to the method (2), in a region where resistivity is comparatively high, the surface of the wafer is brought into the strong inversion state but thermal oxidization is required, thereby inspection cost being increased. Moreover, in the case of an epitaxial wafer, there is presented a problem that the dopant concentration of the interface between the substrate and an epitaxial layer is varied by the heat treatment. The other methods also present the following problems: the strong inversion state cannot be obtained and the wafer is stained by the treatment, so that the measured wafer cannot be shipped as a product wafer as it is. As a result, the present inventor came to recognize that it was difficult to produce the strong inversion state without degrading the quality of the Si wafer.